{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1992:MOAJQVLU2WY2V44JKJHCG2ET6D","short_pith_number":"pith:MOAJQVLU","canonical_record":{"source":{"id":"math/9201261","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"1992-01-01T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"38fe32b9dd0c6fc5e3d913fa95c04c62ec40320681156be1fd359237ae636c39","abstract_canon_sha256":"f1a53054314b96189775383fec666dd76436703b64313b1b78cd78802b0b9cf7"},"schema_version":"1.0"},"canonical_sha256":"6380985574d5b1aaf389524e236893f0e4cb6f50e299535c2470e82408fa443e","source":{"kind":"arxiv","id":"math/9201261","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9201261","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"arxiv_version","alias_value":"math/9201261v1","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9201261","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"pith_short_12","alias_value":"MOAJQVLU2WY2","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"MOAJQVLU2WY2V44J","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"MOAJQVLU","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1992:MOAJQVLU2WY2V44JKJHCG2ET6D","target":"record","payload":{"canonical_record":{"source":{"id":"math/9201261","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"1992-01-01T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"38fe32b9dd0c6fc5e3d913fa95c04c62ec40320681156be1fd359237ae636c39","abstract_canon_sha256":"f1a53054314b96189775383fec666dd76436703b64313b1b78cd78802b0b9cf7"},"schema_version":"1.0"},"canonical_sha256":"6380985574d5b1aaf389524e236893f0e4cb6f50e299535c2470e82408fa443e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:54.611226Z","signature_b64":"jpqEx1G2I56vqzvXbNP19Hy6zosFIB4g9TkKlxQeJESMtwKMprBpf5HKYIq68PFl8GjuFJzOIQKR0U50+jzgDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6380985574d5b1aaf389524e236893f0e4cb6f50e299535c2470e82408fa443e","last_reissued_at":"2026-05-18T01:05:54.610790Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:54.610790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9201261","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X2pTBKRO+4HvpKfTsldE+Ae/zmqNZst2VWpI910SqyQHoSP9xMKmYosaigYNHR9t3wAZg21pPsKlNTNkzkbjCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:22:17.272817Z"},"content_sha256":"b81ac1ec0d2f7b8d72f0aa1e16789e9b6f284a12d27bd7427215fc6e2ddb1f20","schema_version":"1.0","event_id":"sha256:b81ac1ec0d2f7b8d72f0aa1e16789e9b6f284a12d27bd7427215fc6e2ddb1f20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1992:MOAJQVLU2WY2V44JKJHCG2ET6D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A steepest descent method for oscillatory Riemann-Hilbert problems","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Percy Deift, Xin Zhou","submitted_at":"1992-01-01T00:00:00Z","abstract_excerpt":"In this announcement we present a general and new approach to analyzing the asymptotics of oscillatory Riemann-Hilbert problems. Such problems arise, in particular, in evaluating the long-time behavior of nonlinear wave equations solvable by the inverse scattering method. We will restrict ourselves here exclusively to the modified Korteweg de Vries (MKdV) equation,\n  $$y_t-6y^2y_x+y_{xxx}=0,\\qquad -\\infty<x<\\infty,\\ t\\ge0, y(x,t=0)=y_0(x),$$\n but it will be clear immediately to the reader with some experience in the field, that the method extends naturally and easily to the general class of wa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9201261","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kt4nYeXPZ0tFpl6L+WiEVX4sdUUcXBNtjbTbhQFxjASyDrBt7Tvbm+3SvEYre8/RkwUeDI3pArD2K92qIi4yBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:22:17.273159Z"},"content_sha256":"7549ad05edd7de0cd16b6c166ebf866bf8ab80422e9763a4f56521c8ff4a116e","schema_version":"1.0","event_id":"sha256:7549ad05edd7de0cd16b6c166ebf866bf8ab80422e9763a4f56521c8ff4a116e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MOAJQVLU2WY2V44JKJHCG2ET6D/bundle.json","state_url":"https://pith.science/pith/MOAJQVLU2WY2V44JKJHCG2ET6D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MOAJQVLU2WY2V44JKJHCG2ET6D/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T14:22:17Z","links":{"resolver":"https://pith.science/pith/MOAJQVLU2WY2V44JKJHCG2ET6D","bundle":"https://pith.science/pith/MOAJQVLU2WY2V44JKJHCG2ET6D/bundle.json","state":"https://pith.science/pith/MOAJQVLU2WY2V44JKJHCG2ET6D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MOAJQVLU2WY2V44JKJHCG2ET6D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1992:MOAJQVLU2WY2V44JKJHCG2ET6D","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f1a53054314b96189775383fec666dd76436703b64313b1b78cd78802b0b9cf7","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"1992-01-01T00:00:00Z","title_canon_sha256":"38fe32b9dd0c6fc5e3d913fa95c04c62ec40320681156be1fd359237ae636c39"},"schema_version":"1.0","source":{"id":"math/9201261","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9201261","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"arxiv_version","alias_value":"math/9201261v1","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9201261","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"pith_short_12","alias_value":"MOAJQVLU2WY2","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"MOAJQVLU2WY2V44J","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"MOAJQVLU","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:7549ad05edd7de0cd16b6c166ebf866bf8ab80422e9763a4f56521c8ff4a116e","target":"graph","created_at":"2026-05-18T01:05:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this announcement we present a general and new approach to analyzing the asymptotics of oscillatory Riemann-Hilbert problems. Such problems arise, in particular, in evaluating the long-time behavior of nonlinear wave equations solvable by the inverse scattering method. We will restrict ourselves here exclusively to the modified Korteweg de Vries (MKdV) equation,\n  $$y_t-6y^2y_x+y_{xxx}=0,\\qquad -\\infty<x<\\infty,\\ t\\ge0, y(x,t=0)=y_0(x),$$\n but it will be clear immediately to the reader with some experience in the field, that the method extends naturally and easily to the general class of wa","authors_text":"Percy Deift, Xin Zhou","cross_cats":[],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"1992-01-01T00:00:00Z","title":"A steepest descent method for oscillatory Riemann-Hilbert problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9201261","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b81ac1ec0d2f7b8d72f0aa1e16789e9b6f284a12d27bd7427215fc6e2ddb1f20","target":"record","created_at":"2026-05-18T01:05:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f1a53054314b96189775383fec666dd76436703b64313b1b78cd78802b0b9cf7","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"1992-01-01T00:00:00Z","title_canon_sha256":"38fe32b9dd0c6fc5e3d913fa95c04c62ec40320681156be1fd359237ae636c39"},"schema_version":"1.0","source":{"id":"math/9201261","kind":"arxiv","version":1}},"canonical_sha256":"6380985574d5b1aaf389524e236893f0e4cb6f50e299535c2470e82408fa443e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6380985574d5b1aaf389524e236893f0e4cb6f50e299535c2470e82408fa443e","first_computed_at":"2026-05-18T01:05:54.610790Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:54.610790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jpqEx1G2I56vqzvXbNP19Hy6zosFIB4g9TkKlxQeJESMtwKMprBpf5HKYIq68PFl8GjuFJzOIQKR0U50+jzgDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:54.611226Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9201261","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b81ac1ec0d2f7b8d72f0aa1e16789e9b6f284a12d27bd7427215fc6e2ddb1f20","sha256:7549ad05edd7de0cd16b6c166ebf866bf8ab80422e9763a4f56521c8ff4a116e"],"state_sha256":"23131fa53a6745007e2093c878d04886b76f2f0b2a6cd8f449473b93bc9d9f99"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5x/U/tirR6afC7rXx0s5mKO1ISnqBHR/7dolt/goRkphhNwr7QUs5NQ+KCxlzUU4HpnNinoMsZxA3dYp4tzPDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T14:22:17.275058Z","bundle_sha256":"d49ba0b951db52be637a21a1262caabc397ac08bda2e5c762d6d785ea3225b86"}}